In this paper, we introduce a symbolic approach to the problem of identity testing algebraic integers in the number field generated over \(\mathbb {Q}\)  by real radicals; given an algebraic circuit representing a multivariate polynomial \(f(x_1,\ldots ,x_k)\in \mathbb {Z}[x_1,\ldots ,x_k]\) , and radical inputs \(\@root d_1 \of { a_1},\ldots ,\@root d_k \of { a_k}\)  where the radicands \(a_i\) , and exponents \(d_i\)  are nonnegative integers, the Radical Identity Testing (RIT) problem is to decide whether \(f(\@root d_1 \of { a_1},\ldots ,\@root d_k \of { a_k}) = 0\) . The problem is easily seen to admit a PSPACE upper bound by a reduction to the existential theory of reals [1]}: introduce a new formal variable for every gate of the circuit, add the equations \(x^{d_i} - a_i = 0\)  and \(x_i > 0\)  for every radical; RIT is now decided by checking if the resulting system of polynomial equations has a solution over the real numbers.
